In MRI technologies, the imaging speed is a very important parameter. Several hours were generally required for an examination in early stages of the technology, and since then the imaging speed has been increased quite significantly owning to the technical improvements in relation to field intensity, gradient hardware and pulse sequences. However, fast changes of field gradient and high density continuous radio frequency (RF) pulses would result in a specific absorption rate (SAR) and the amount of heat generated in organs and tissues which have become unbearably beyond human physiological limits, therefore increasing the imaging speed has met a bottleneck.
Thereafter, researchers found that the speed of magnetic resonance imaging could be greatly increased by virtue of the application of complicated computer aided image reconstruction algorithms together with cooperated coil array, and such a technology was commonly referred to as parallel imaging technology. The reconstruction of parallel-acquired images is a technology for image reconstruction using parallel acquisition, which utilizes the differences in the spatial sensitivities between phase-controlled arrayed coils to perform spatial encoding and utilizes the phase-controlled arrayed coils to acquire data simultaneously, so that when compared with the imaging speed of conventional MRI it obtained an imaging speed of 2 to 6 times higher or even more. By adopting the parallel imaging technology, it has brought forward new requirements to MRI systems; for example, there are needs for multiple receiving channels, multi-arrayed coils and calibration of the sensitivities of the coils, the use of special data processing and image reconstructing methods and so on.
Parallel imaging can increase image acquisition speed and the increase of imaging speed is achieved by reducing the filling rate in the K-space. However, if the filling rate in the K-space is below the limit of the sampling theorem, it would lead to the appearance of artifacts in the images reconstructed by using direct Fourier reconstruction. The images of common MRI are obtained by acquiring an object's information in frequency domain which is subject to Fourier transform. According to the sampling theorem, an object's repeat cycle in the image domain is in inverse proportion to the sampling interval in the frequency domain. If an image's spatial repeat cycle is smaller than the size of the image itself, the reconstructed images will be superposed, and this phenomenon is referred to as overlapping in signal processing. If the sampling intervals in phase encoding direction are equal to the reciprocal of the FOV in the phase encoding direction, it will be just right for the images not to overlap, and in this case the sampling in the K-space is referred to as full-sampling. When the sampling is done with sampling intervals greater than 1/FOV, it is referred to as under-sampling, that is to say, the K-space information acquired is not sufficient for reconstructing a complete image, and such under-sampling will cause image overlapping; when it is done in the opposite way, then it is called over-sampling which will not cause image overlapping. FIG. 1 shows illustrative images of full-sampling and under-sampling, in which the left-hand one is the full-sampling and the right-hand one is the under-sampling. In FIG. 1 the vertical direction is the phase encoding direction, the left image is full-sampling, and the sampling intervals in the phase encoding direction are Δky; while the right image is ½ under-sampling, the sampling intervals in the phase encoding direction are 2Δky.
During MRI imaging, the magnetic resonance signals of tissues are acquired by a receiving coil. FIG. 2 shows the images obtained by the full-sampling and under-sampling in the phase encoding direction shown in FIG. 1. In FIG. 2, the vertical direction is the direction of phase, and the horizontal direction is the direction of frequency. As shown in FIG. 2, the left image is obtained by full-sampling with the sampling intervals of Δky; while the right image is obtained by ½ under-sampling with the sampling intervals of 2Δky. As shown in the right image, if two adjacent surface coils (coil 1 and coil 2) are used to sample and acquire respectively the data from the object in the drawing, and the sampling rate in the phase encoding direction is 2/FOV, then after direct reconstruction two images with superposed artifacts will be obtained, and the field of view of each image will be FOV/2, but each image will contain the contents of the other image, that is to say, the value of each pixel in the right image is constituted by the contributions of two object units of the origin image, for example, the signal intensity of the pixel 1 in the right image is constituted by the contributions of two object units 1 and 2 in the left image, likewise, the signal intensity of the pixel 2 in the right image is also constituted by the contribution of two object units 2 and 1 in the left image. It is not difficult to see in the right image that the signal intensity of the artifact is weaker than the signal intensity of the origin image, this is because that is the sample's spinning signal is weighted by the sensitivity function of the coils, while the amplitude of the sensitivity function of a surface coil is relatively small in the area far from the coil. The overlapping caused by sampling depends on the way that the K-space is filled, i.e. the tracks in the K-space. The abovementioned artifacts are ones caused by uniform grid under-sampling, as to helical tracks, the artifacts caused by under-sampling will be very irregular.
As to multi-coil acquisition, although the K-space information acquired by each coil is not sufficient, the differences between the signals acquired by different coils can be utilized and processed to obtain a complete image. The reconstruction algorithms for eliminating overlapped artifacts for parallel imaging can be divided roughly into two categories: the simultaneous acquisition of spatial harmonics technique (SMASH) and the sensitivity encoding parallel acquisition technique (SENSE). Among them, SMASH method is a method using the sensitivity functions of various channel coils to form spatial harmonics and to perform assistant encoding. The sensitivity function of an ordinary coil is of slow variation and can be regarded as a Gaussian distribution function, and then a linear combination of the sensitivity functions of various channel coils can be used to form spatial harmonics of a certain frequency. And the spatial harmonic function is used to make up a phase encoding line whose data are not actually acquired.
Differing from the solution of SMASH for processing in the frequency domain, the SENSE method eliminates the artifacts caused by under-sampling by solving the linear equation set in the image domain. Because the superposition effects resulted from the image's spatial cycles, for example, when the sampling rate is ½ of the full-sampling, the value of each pixel of the image obtained directly by Fourier transform is constituted by the contributions of two object units in the origin image. This can be expressed by formula (1):s1=p11m1+p12m2  (1)
Formula (1) can be explained with reference to FIG. 2: the value of point 1 in the right image is determined by the sum of the product of the magnetization intensity m1 of the object unit 1 in the left image and the sensitivity P11 of the coil 1 at point 1 and the product of the magnetization intensity m2 of the object unit 2 and the sensitivity P12 of the coil 1 at point 2. The P11 and P12 are measurable quantities and two equations are needed to work out m1 and m2, that is to say the data measured by at least two individual coils are needed. If expressed with a matrix, it is:
                              [                                                                      s                  1                                                                                                      s                  2                                                              ]                =                              [                                                                                                      p                                              1                        ⁢                                                                                                  ⁢                        1                                                              ,                                          p                      21                                                                                                                                                              p                      12                                        ,                                          p                      22                                                                                            ]                    ·                      [                                                                                m                    1                                                                                                                    m                    2                                                                        ]                                              (        2        )            wherein s2 is the value of the point 2 in the right image, p21 and p22 are defined the same as above. The formula (2) can be further expressed as:S=PM  (3)wherein S is the vector of Nc×1, and Nc is the number of channels. M is the vector of Np×1, and Np is the under-sampling rate. The origin image is obtained by working out the inverse of P. In the case that the number of channels is greater than the under-sampling rate, in the equation (3) Nc>Np, and this is a redundant linear equation set, that is, the number of known conditions is larger than that of unknown quantities. Generally the optimum solution is achieved by working out the plus inverse of P.{circumflex over (M)}=(PHP)−1PHS=WS  (4)wherein the matrix W is referred to as a weighted matrix, and the upper superscript H represents the conjugate transpose.
In a RF electromagnetic field, a human body is regarded as a load, there will be variations in a coil's sensitivity function when measuring different human bodies, and these variations are sufficient to affect the quality of reconstructed image, therefore a coil's sensitivity is generally needed to be acquired in real-time. When collecting data the SENSE method performs full-sampling in the central region of K-space and performs under-sampling in peripheral regions. Thus the origin data of the k-space are divided into two parts: uniform under-sampled data and low frequency fully-sampled data. The uniform under-sampled data are used to generate an overlapped image, while the low frequency fully-sampled data are used to generate a blurred image of tissues and further to obtain the coil's real-time sensitivity distribution and a weighted matrix, and finally, the overlapped image produced with the uniform under-sampled data is synthesized with the weighted matrix obtained from the low frequency fully-sampled data, so as to obtain an image of high resolution without overlapping. Here, the low frequency fully-sampled data for obtaining the coil's sensitivity distribution and the weighted matrix are referred to as reference data, the low frequency fully-sampled phase encoding lines in the K-space are referred to as reference lines.
The advantage of increasing imaging speed by parallel acquisition conducted with multi-channel coils is obvious. Given the same sampling time, the parallel acquisition technology can also be used to increase the resolution of an image. The parallel acquisition also has some additional benefits, for example it is able to reduce the image artifacts resulted from off-resonance. Meanwhile, because of the speed increase, the parallel acquisition technology can also reduce artifacts by movements.
However, there is a cost to pay for realizing the parallel acquisition. First, since the data actually acquired are reduced, although an overlapping-free image can be reconstructed by using parallel acquisition reconstruction technology, the signal to noise ratio is the 1/√{square root over (Nf)} of that of the image by full-sampling under the same hardware conditions, wherein Nf is an accelerating factor, therefore, the larger is the accelerating factor, the bigger is the loss of the image quality, that is, the bigger is the drop of the signal to noise ratio (SNR).